A generalization of Sen-Brinon's theory

作者：Yamauchi Takuya^*

来源：Manuscripta Mathematica, 2010, 133(3-4): 327-346.

DOI：10.1007/s00229-010-0372-2

Let K be a complete discrete valuation field of mixed characteristic and k be its residue field of prime characteristic p > 0. We assume that [k : k (p) ] = p (h) < a. Let G (K) be the absolute Galois group of K and R be a Banach algebra over C(p) := <(<(K)over bar>)over cap>with a continuous action of G (K) . When k is perfect (i.e. h = 0), Sen studied the Galois cohomology H(1)(G(K), R*) and Sen's operator associated to each class (Sen Ann Math 127:647-661, 1988). In this paper we generalize Sen's theory to the case h >= 0 by using Brinon's theory (Brinon Math Ann 327:793-813, 2003). We also give another formulation of Brinon's theorem (A la Colmez).

• 出版日期2010-11